Xr. Chen et Mz. Jin, STRONG CONSISTENCY UNDER GAUSS-MARKOV CONDITION, Science in China. Series A, Mathematics, Physics, Astronomy & Technological Sciences, 39(2), 1996, pp. 137-147
Let Y-i=x(i)' beta+e(i), 1 less than or equal to i less than or equal
to n, be a linear model, <(beta)over cap>(n)=(<(beta)over cap>(n1), ..
., <(beta)over cap>(np)) be the LS estimate of beta-(beta(1), ..., bet
a(p))'. Denote by u(n) the (1,1)-element of [GRAPHICS] Assume that Ee(
i)=0 and {e(i)} obeys the Gauss-Markov condition Ee(i)e(j)=sigma(2) de
lta(ij). It is shown that [GRAPHICS] is a sufficient condition for <(b
eta)over cap>(n1) to be strongly consistent. This condition is accurat
e in the sense that for any e(n) --> 0, the condition[GRAPHICS] ceases
to be sufficient. Some remarks are made concerning the necessary and/
or sufficient condition for <(beta)over cap>(n1) to be strongly consis
tent.